Reduced SL(2,R) WZNW Quantum Mechanics

TL;DR

This paper investigates the quantum mechanics of a reduced $SL(2, )$ WZNW model, revealing its spectrum, eigenfunctions, and the structure of its phase space after classical reduction, with implications for understanding constrained quantum systems.

Contribution

It provides a detailed analysis of the quantum properties of the $SL(2, )$ WZNW model after classical reduction, including spectrum and eigenfunctions, which was previously unexplored.

Findings

Derived the spectrum and eigenfunctions of the reduced model.

Analyzed the phase space structure and its quantum implications.

Discussed the connection between different parts of the reduced configuration space.

Abstract

The $SL(2,\R)$ WZNW $\rightarrow$ Liouville reduction leads to a nontrivial phase space on the classical level both in $0+1$ and $1+1$ dimensions. To study the consequences in the quantum theory, the quantum mechanics of the $0+1$ dimensional, point particle version of the constrained WZNW model is investigated. The spectrum and the eigenfunctions of the obtained---rather nontrivial---theory are given, and the physical connection between the pieces of the reduced configuration space is discussed in all the possible cases of the constraint parameters.